Krsna is always complete as Himself and therefore NEVER alone.

This is because Krsna divides Himself into two - Srimati Radharani and Krsna.

And when Radha and Krsna unite in one body, that is Lord Caitanya Mahaprabhu.

Krsna is always enjoying in Vrindavana with His consort Srimati Radharani, who Krsna created by dividing Himself into two, just so He could experience loving intimate exchanges with a women.

Krsna is never alone because He is "fully complete" as Himself due to always enjoying with His internal potency led by the personification of the internal energy, Srimati Radharani.

Krsna also expands Himself as His Visnu-tattva expansions, who are the unlimited Visnu/Narayana Forms of God who have their own perpetual Vaikuntha Planet that take up 3/4 of the Spiritual Sky.

Krsna also expands as Karanarnavasayi Visnu (Maha-Visnu), Garbhodakashayi Visnu and Ksirodakasayi Visnu (Paramatma) to maintain the material creation.

For material creation, Lord Krsna's plenary expansion assumes three Visnus as said above.

The first is Karanarnavasayi Visnu (Mahā Viṣṇu) who creates the total material energy known as the mahat-tattva.

The second is Garbhodakaśāyī Viṣṇu who enters deep into all the massive Brahmanda universes and creates an inner secondary smaller material universe.

The third is Kṣīrodakaśāyī Visnu, who is the all-pervading super-soul accompanying each marginal living entity (jiva-soul) within each inner material universe existing deep inside each Brahmanda universal covering. Kṣīrodakaśāyī Visnu is in the heart of every marginal living entity (jiva-soul) and is known as Paramātmā.

He is present even within the atoms. The goal of life is to know Kṛṣṇa, who is situated within the heart of every living being as Paramātmā, the four-handed Viṣṇu form.

In Srimad Bhagavatam, this is explained as-

Kāraṇārṇavaśāyī Viṣṇu (Maha Visnu) is the first incarnation of the Supreme Lord, and He is the master of eternal time, space, cause and effects, mind, the elements, the material ego, the modes of nature, the senses, the universal form of the Lord.

Garbhodhakaśāyī Viṣṇu is an expansion of Mahā Viṣṇu who expands from Nārāyaṇa/Visnu in Vaikuṇṭha.

Garbhodhakaśāyī Visnu is the form of Pradyumna within the material universe. He is the father of Brahmā who appeared from His navel.

Garbhodakashayi Visnu is also called Hiraņyagarbha.

Each Form has a different role in the maintenance of the temporary material universes, known as Brahmanda universes, that take up 1/4 of the Spiritual Sky.

There are also other expansions of Krsna who are NOT Visnu-tattva, like Siva-tattva (Lord Siva), and jiva-tattva, (jiva-souls who are the independent marginal living entities) 

The "marginal living entities" have their own free will and independence in Goloka Vrindavana that allows them to voluntarily choose for themselves how to serve Krsna, or even reject Him if they choose. 

Marginal potency means free will. 

There are many varieties of living entities in the Spiritual Sky and manifest in different categories of Krsna's energies but can NEVER be separated from Krsna.

They are Viṣṇu-tattva, Sakti-Visnu-tattva, Siva-tattva and the marginal living entities (jiva-tattva souls) 

Just like the Sun-disc can NEVER be separated from the sun-rays similarly, Krsna is NEVER without the various grades of living entities mentioned above.

Krsna is NEVER alone due to EVERYTHING being completely situated within Him.

Krsna is the Supreme Personality of Godhead and cause of ALL causes. The 'cause of ALL causes' is significant here - meaning EVERYTHING IS in Krsna.

Kṛṣṇa is simultaneously an independent Person from all the variety of different expansions. 

This is Krsna's full potential.

He is the Supreme controller, fully satisfied in Himself because everything is in Him and everything is part and parcel of Krsna.

Therefore Krsna can NEVER be alone.

This should be properly understood so one can know why Krsna can NEVER be alone.  

Krsna IS the Supreme Lord as His own individual bodily (vigraha) Form, yet simultaneously ALL living entities depend on Krsna a

for their existence just like the Sun-rays depend on the presence of Sun to exist.

Srila Prabhupada - "Rādhā and Kṛṣṇa are "one and the same", but They have assumed two bodies. Thus They enjoy each other, tasting the mellows of love.

The two transcendentalists Rādhā and Kṛṣṇa are a puzzle to materialists. 

The description of Rādhā and Kṛṣṇa from the diary of Śrīla Svarūpa Dāmodara Gosvāmī is a condensed explanation, but one needs great spiritual insight to understand the mystery of these two personalities.

One is enjoying in two.

Śrī Kṛṣṇa is the potent factor, and Śrīmatī Rādhārāṇī is the internal potency.

According to Vedānta philosophy, there is no difference between the potent and the potency; they are identical. We cannot differentiate between one and the other, any more than we can separate fire from heat.

Everything in the Absolute is inconceivable in relative existence. Therefore in relative cognizance it is very difficult to assimilate this truth of the oneness between the potent and the potency.

The philosophy of inconceivable oneness and difference propounded by Lord Caitanya is the only source of understanding for such intricacies of transcendence.

In fact, Rādhārāṇī is the internal potency of Śrī Kṛṣṇa, and She eternally intensifies the pleasure of Śrī Kṛṣṇa. 

Impersonalists cannot understand this without the help of a mahā-bhāgavata devotee.

The very name “Rādhā” suggests that Śrīmatī Rādhārāṇī is eternally the topmost mistress of the comforts of Śrī Kṛṣṇa. As such, She is the medium transmitting the living entities’ service to Śrī Kṛṣṇa.

Devotees in Vṛndāvana therefore seek the mercy of Śrīmatī Rādhārāṇī in order to be recognized as loving servitors of Śrī Kṛṣṇa". (Caitanya Caritamrita Adi 4.56, Translation and Purport)

Srila Prabhupada - "When Krsna wants to be attracted by a woman, He has to create such a woman from His own energy. That woman is Rādhārāṇī". (Srimad Bhagavatam Canto 3 Chapter 31 text 38 Purport)

Krsna divided Himself into "two" so He could experience loving exchanges. 

For even Krsna, love can NEVER exist when there is just "one", there MUST be "two" and they are Srimati Radharani and Krsna.

Therefore when Krsna wanted to experience loving emotions and affection with a women He divided Himself into "two", Radha and Krsna just so He could experience loving exchanges.

Madhudviṣa Swami - "Śrīla Prabhupāda, you spoke of inferior energy and superior energy. Those are two general categories. Are there other categories of energies besides that, and specifically how could we understand Śrīmatī Rādhārāṇī Is She...?"

Srila Prabhupāda - "She is spiritual energy".

Madhudviṣa Swami - "But is She jīva-bhūta or?"

Srila Prabhupada - "No, no, no. She is Kṛṣṇa. If everything is Kṛṣṇa and Rādhārāṇī is not Kṛṣṇa, what is that? Kṛṣṇa. He (She) is Kṛṣṇa. She is the Kṛṣṇa's pleasure potency".

Madhudviṣa Swami - "She is not jīva?"

Srila Prabhupada - "No, no, no. She is Kṛṣṇa. Kṛṣṇa divided Himself into His energy and Himself. That energy, original spiritual energy, is Rādhārāṇī. 

That is stated by Jīva Gosvāmī. Rādhā kṛṣṇa-praṇaya-vikṛtir hlādinī śaktir asmāt. When Kṛṣṇa wants pleasure, He cannot accept the inferior energy. AThe same superior energy, Kṛṣṇa, is divided into two. 

That is Rādhā and Kṛṣṇa. 

And again, when they unite, that is Caitanya Mahāprabhu. Divided, they are Rādhā and Kṛṣṇa, and united, Caitanya Mahāprabhu. 

Śrī-kṛṣṇa-caitanya rādhā-kṛṣṇa nahe anya. Anya means another. 

So Śrī Kṛṣṇa Caitanya is combination of Rādhā and Kṛṣṇa. And when they are divided into two, that is Rādhā and Kṛṣṇa. 

This is the purport. Rādhā kṛṣṇa-praṇaya-vikṛtir hlādinī śaktir asmād ekātmānāv api bhuvi purā deha-bhedaṁ gatau tau, śrī-caitanyākhyaṁ prakaṭam adhunā tad-dvayaṁ caikyam āptam [Cc. Ādi 1.5]. 

These are the conclusion-

Śrī Caitanya Mahāprabhu is the combination of Rādhā and Kṛṣṇa, where Krsna experiences Himself as Rādhārāṇī to understand Radharani. This is Caitanya Mahāprabhu.

Rādhārāṇī is the chief gopī and all Her young girl friends, they are also gopīs. (Lecture on SB 2.1.1-5 -- Melbourne, June 26, 1974)

"Rādhikā is the transformation of Kṛṣṇa’s love. She is His internal energy called hlādinī". (Caitanya Caritamrita Adi 4.59, Translation)

Srila Prabhupada - "Radharani's mind, senses and body are steeped in love for Kṛṣṇa. She is Kṛṣṇa’s own energy, and She helps Him in His pastimes.

Śrīmatī Rādhārāṇī is as fully spiritual as Kṛṣṇa. No one should consider Her to be material. 

She is definitely not like the conditioned souls, who have material bodies, gross and subtle, covered by material senses.

She is all-spiritual, and both Her body and Her mind are of the same spiritual embodiment. 

Because Her body is spiritual, Her senses are also spiritual. Thus Her body, mind and senses fully shine in love of Kṛṣṇa.

She is the personified hlādinī-śakti (the pleasure-giving energy of the Lord’s internal potency), and therefore She is the only source of enjoyment for Śrī Kṛṣṇa.

Kṛṣṇa cannot enjoy anything that is internally different from Him. Therefore Rādhā and Śrī Kṛṣṇa are identical. 

The sandhinī portion of Śrī Kṛṣṇa’s internal potency has manifested the all-attractive form of Śrī Kṛṣṇa, and the same internal potency, in the hlādinī feature, has presented Śrīmatī Rādhārāṇī, who is the attraction for the all-attractive. 

No one can match Śrīmatī Rādhārāṇī in the transcendental pastimes of Śrī Kṛṣṇa". (Caitanya Caritamrta Adi 4.71, Translation and Purport)

"Just as the fountainhead, Lord Kṛṣṇa, is the cause of all incarnations, so Śrī Rādhā is the cause of all these consorts". (Caitanya Caritamrita Adi 4.76, Translation)

"Rādhā is the one who gives pleasure to Govinda, and She is also the enchantress of Govinda. She is the be-all and end-all of Govinda, and the crest jewel of all His consorts".(Caitanya Caritamrita Adi 4.82, Translation)

"The transcendental goddess Śrīmatī Rādhārāṇī is the direct counterpart of Lord Śrī Kṛṣṇa. She is the central figure for all the goddesses of fortune. She possesses all the attractiveness to attract the all-attractive Personality of Godhead. She is the primeval internal potency of the Lord". (Caitanya Caritamrta Adi 4.83, Translation)

Srila Prabhupada - "When Krsna wants to be attracted by a woman, He has to create such a woman from His own energy. That woman is Rādhārāṇī.

It is explained by the Gosvāmīs that Rādhārāṇī is the manifestation of the pleasure potency of the Supreme Personality of Godhead.

When the Supreme Lord wants to derive transcendental pleasure, He has to create a woman from His internal potency and that women is Srimati Radharani" (Srimad Bhagavatam Canto 3 Chapter 31 text 38, Purport)

Sri Krsna - "Among the gopīs, You, Śrīmatī Rādhārāṇī, are the chief. Therefore You are the very life of My life and center of all Vṛndāvana’s activities". (Caitanya Caritamrta Madhya 13.150, Translation)

Srila Prabhupada - "From Kṛṣṇa’s own statement above, it appears that Rādhārāṇī is the Queen of Vṛndāvana and that Kṛṣṇa is simply Her decoration. Kṛṣṇa is known as Madana-mohana, the enchanter of Cupid, but Śrīmatī Rādhārāṇī is the enchanter of Kṛṣṇa.

Consequently Śrīmatī Rādhārāṇī is called Madana-mohana-mohinī, the enchanter of the enchanter of Cupid". (Caitanya Caritamrta Madhya 13.150, Translation and Purport)

"Simultaneously one and difference" philosophy is the teachings of Lord Krsna Caitanya Mahaprabhu.

"Lord Śrī Kṛṣṇa is the reservoir of all pleasure, and Śrīmatī Rādhārāṇī is the personification of ecstatic love of Godhead. These two forms had combined as one in Śrī Caitanya Mahāprabhu. This being the case, Lord Śrī Caitanya Mahāprabhu revealed His real form to Rāmānanda Rāya". (Caitanya Caritamrta Madhya 8.282, Translation)

Sri Caitanya Mahāprabhu -“I have now converted My body and mind into the ecstasy of Śrīmatī Rādhārāṇī; thus I am tasting My own personal sweetness in that form.” (Caitanya Caritamrta Madhya 8.288, Translation)

Srila Prabhupada -"Gaurasundara above informed Śrī Rāmānanda Rāya, 'My dear Rāmānanda Rāya, you were actually seeing a separate person with a fair-complexioned body. Actually I am not fair. Being Śrī Kṛṣṇa, the son of Nanda Mahārāja, I am blackish, but when I come in touch with Śrīmatī Rādhārāṇī I become fair-complexioned externally. 

Śrīmatī Rādhārāṇī does not touch the body of anyone but Kṛṣṇa. I taste My own transcendental features by accepting the complexion of Śrīmatī Rādhārāṇī. Without Rādhārāṇī, one cannot taste the transcendental pleasure of Kṛṣṇa’s conjugal love.'

In this regard, Śrīla Bhaktisiddhānta Sarasvatī Ṭhākura comments on the prākṛta-sahajiyā-sampradāya, which considers Kṛṣṇa and Lord Caitanya to possess different bodies. They misinterpret the words gaura aṅga nahe mora in text 287. 

From that verse and the present verse we can understand that Lord Caitanya Mahāprabhu is nondifferent from Kṛṣṇa, both are the same Supreme Personality of Godhead. 

In the form of Kṛṣṇa, the Lord enjoys spiritual bliss and remains the shelter of all devotees, viṣaya-vigraha.

And in His Gaurāṅga feature Kṛṣṇa tastes separation from Kṛṣṇa in the ecstasy of Śrīmatī Rādhārāṇī.

This ecstatic form is Śrī Kṛṣṇa Caitanya. Śrī Kṛṣṇa is always the transcendental reservoir of all pleasure, and He is technically called dhīra-lalita.

Śrīmatī Rādhārāṇī is the embodiment of spiritual energy, personified as ecstatic love for Kṛṣṇa; therefore only Kṛṣṇa can touch Her.

The dhīra-lalita aspect is not seen in any other form of the Lord, including Viṣṇu and Nārāyaṇa.

Śrīmatī Rādhārāṇī is therefore known as Govinda-nandinī and Govinda-mohinī, for She is the only source of transcendental pleasure for Śrī Kṛṣṇa and the only person who can enchant His mind". (Caitanya Caritamrta Madhya 8.288, Translation and Purport)

Sri Krsna - “My dearest Śrīmatī Rādhārāṇī, please hear Me. I am speaking the truth. I cry day and night simply upon remembering all you inhabitants of Vṛndāvana. No one knows how unhappy this makes Me.” (Caitanya Caritamrta Madhya 13.149, Translation) 

Srila Prabhupada - "It is said: vṛndāvanaṁ parityajya padam ekaṁ na gacchati.

In one sense, Kṛṣṇa, the original Personality of Godhead (īśvaraḥ paramaḥ kṛṣṇaḥ sac cid ānanda vigrahaḥ [Bs. 5.1]), does not even take one step away from Vṛndāvana. However, in order to take care of various duties, Kṛṣṇa had to leave Vṛndāvana.

He had to go to Mathurā to kill Kaṁsa, and then He was taken by His father to Dvārakā, where He was busy with state affairs and disturbances created by demons. 

Kṛṣṇa was away from Vṛndāvana, and He was not at all happy, as He plainly disclosed to Śrīmatī Rādhārāṇī. 

She is the dearmost life and soul of Śrī Kṛṣṇa, and He expressed His mind to Her as follows". (Caitanya Caritamrta Madhya 13.149, Translation and Purport)

Srila Prabhupada - "Śrī Kṛṣṇa continued: “All the inhabitants of Vṛndāvana-dhāma—My mother, father, cowherd boyfriends and everything else—are like My life and soul.

And among all the inhabitants of Vṛndāvana, the gopīs are My very life and soul. And among the gopīs, You, Śrīmatī Rādhārāṇī, are the chief. Therefore You are the very life of My life. 

Śrīmatī Rādhārāṇī is the center of all Vṛndāvana’s activities. In Vṛndāvana, Kṛṣṇa is the instrument of Śrīmatī Rādhārāṇī; therefore all the inhabitants of Vṛndāvana still chant “Jaya Rādhe!”

From Kṛṣṇa’s own statement given herein, it appears that Rādhārāṇī is the Queen of Vṛndāvana and that Kṛṣṇa is simply Her decoration. Kṛṣṇa is known as Madana mohana, the enchanter of Cupid, but Śrīmatī Rādhārāṇī is the enchanter of Kṛṣṇa.

Consequently Śrīmatī Rādhārāṇī is called Madana-mohana-mohinī, the enchanter of the enchanter of Cupid". (Caitanya Caritamrta Madhya 13.150, Translation and Purport)

"Of all the gopīs, Śrīmatī Rādhārāṇī is the chief. She is a jewel mine of ecstatic love and the source of all purified transcendental conjugal mellows". (Caitanya Caritamrta Madhya 14.160, Translation)

"Of all the gopīs, Rādhārāṇī is the dearmost. Similarly, the lake known as Rādhā-kuṇḍa is very dear to the Lord because it is very dear to Śrīmatī Rādhārāṇī". (Caitanya Caritamrta Madhya 18.7, Translation)

"Lord Kṛṣṇa, the Supreme Personality of Godhead, who appeared as the son of Nanda Mahārāja, is the supreme hero in all dealings. 

Similarly, Śrīmatī Rādhārāṇī is the topmost heroine in all dealings". (Caitanya Caritamrta Madhya 23.66, Translation)

Srila Prabhupada - "Viṣaya and āśraya are two very significant words relating to the reciprocation between Kṛṣṇa and His devotee.

The devotee is called the āśraya, and his beloved, Kṛṣṇa, is the viṣaya.

Different ingredients are involved in the exchange of love between the āśraya and viṣaya, which are known as vibhāva, anubhāva, sāttvika and vyabhicārī.

Vibhāva is divided into the two categories ālambana and uddīpana. Ālambana may be further divided into āśraya and viṣaya.

In the loving affairs of Rādhā and Kṛṣṇa, Rādhārāṇī is the āśraya feature and Kṛṣṇa the viṣaya.

The transcendental consciousness of the Lord tells Him -

“I am Kṛṣṇa, and I experience pleasure as the viṣaya. The pleasure enjoyed by Rādhārāṇī, the āśraya, is many times greater than the pleasure I feel.”

Therefore, to feel the pleasure of the āśraya category, Lord Kṛṣṇa appeared as Śrī Caitanya Mahāprabhu". (Caitanya Caritamrta Adi 4.135, Purport)

Srila Prabhupada - "Among the gopīs, Śrīmatī Rādhikā is the foremost. She surpasses all in beauty, in good qualities, in good fortune and, above all, in love.

Among all the gopīs, Śrīmatī Rādhārāṇī is the most exalted. She is the most beautiful, the most qualified and, above all, the greatest lover of Kṛṣṇa". (Caitanya Caritamrta Adi 4.214, Translation and Purport)

"Rādhā is the beloved consort of Kṛṣṇa, and She is the wealth of His life. Without Her, the gopīs cannot give Him pleasure". (Caitanya Caritamrta Adi 4.218, Translation)

Srila Prabhupada - "Distinguishing between pure devotees and internal or confidential devotees, Śrī Rūpa Gosvāmī, in his book Upadeśāmṛta, traces the following gradual process of development.

Out of many thousands of karmīs, one is better when he is situated in perfect Vedic knowledge.

Out of many such learned scholars and philosophers, one who is actually liberated from material bondage is better, and out of many such persons who are actually liberated, one who is a devotee of the Supreme Personality of Godhead is considered to be the best.

Among the many such transcendental lovers of the Supreme Personality of Godhead, the gopīs are the best, and among the gopīs Śrīmatī Rādhikā is the best.

Śrīmatī Rādhikā is very dear to Lord Kṛṣṇa, and similarly Her ponds, namely, Śyāma-kuṇḍa and Rādhā-kuṇḍa, are also very dear to the Supreme Personality of Godhead". (Caitanya Caritamrta Adi 7.18-19, Purport)

"Kṛṣṇa’s desire in the rāsa-līlā circle is perfectly complete, but Śrīmatī Rādhārāṇī is the binding link in that desire".(Caitanya Caritamrita Madhya-lila 8.113, Translation)

“The body of Śrīmatī Rādhārāṇī is a veritable transformation of love of Godhead; She is the dearmost friend of Kṛṣṇa, and this is known throughout the world". (Caitanya Caritamrta Madhya 8.162, Translation)

"That supreme ecstasy of Śrīmatī Rādhārāṇī is the essence of spiritual life. Her only business is to fulfill all the desires of Kṛṣṇa". (Caitanya Caritamrta Madhya 8.164, Translation)

"Śrīmatī Rādhārāṇī is the topmost spiritual gem, and the other gopīs—Lalitā, Viśākhā and so on-are expansions of Her spiritual body". (Caitanya Caritamrta Madhya 8.165, Translation)

Srila Prabhupada - "In his Amṛta pravāha bhāṣya, Śrīla Bhaktivinoda Ṭhākura states -

“Śrīmatī Rādhārāṇī is the creeper of love of Godhead, and the gopīs are exactly like twigs, flowers and leaves.

When water is sprinkled on the creeper, the twigs, flowers and leaves indirectly receive all the benefits of the creeper itself.

But water sprinkled directly on the twigs, leaves and flowers is not as effective as water sprinkled on the creeper’s root.

The gopīs are not as pleased when they directly mix with Kṛṣṇa as when they serve to unite Śrīmatī Rādhārāṇī with Kṛṣṇa. 

Their transcendental pleasure lies in uniting Them.” Of all the gopīs, Śrīmatī Rādhārāṇī is the topmost". (Caitanya Caritamrta Madhya 8.210, Purport)

Srila Prabhupada - "In the Ādi Purāṇa the Supreme Personality of Godhead Himself says-

na tathā me priyatamo brahmā rudraś ca pārthiva na ca lakṣmīr na cātmā ca yathā gopī-jano mama

“Lord Brahmā, Lord Śiva, the goddess of fortune and even My own self are not as dear to Me as the gopīs.”

Of all the gopīs, Śrīmatī Rādhārāṇī is the topmost. Rūpa Gosvāmī and Sanātana Gosvāmī are the most exalted servitors of Śrīmatī Rādhārāṇī and Lord Śrī Caitanya Mahāprabhu.

Those who adhere to their service are known as rūpānuga devotees". (Caitanya Caritamrta Madhya 8.246, Purport)*^*