We know that there is a God(devatā) of sun(Surya deva). And when sun dies it becomes a black hole.So is there a God of black hole.
It's kind of a scientific question with a religious tarka(twist) to it, so let me explain it in both ways as much as I can.: (Though there is no direct answer to it, so I will just have speculate it like 1 + 1 = 2 kind of a mathematical way).
"A black hole is a region of spacetime where gravity is so strong that nothing—no particles or even electromagnetic radiation such as light—cant escape from it. The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole."
Lord Shiva is the Guru of gurus in his dakshinamurti form. Guru means some teacher, influencer who attracts and guide people. Lord shiva is also the kameshwaram in this form he is the lord of attraction. So combining this two tattwas of lord shiva we get the Guru tattwa from lord dakshina Murthy and akarshan tattwa from lord madan kameshwara. Thus Guru tattwa + akarshan = guruttwa akarshan which means gravity so lord shiva is the lord of gravity.
Dakshinamurti as the guru of gurus even the guru of lord brahma himself."
“yo devaanaaM prabhavashchodbhavashcha vishvaadhipo rudro maharshhiH | hiraNyagarbha.n janayaamaasa puurva.n sa no buddhyaa shubhayaa sa.nyunaktu ||” (Svetaswatara Upanishad 3:04)
“He, the omniscient Rudra, the creator of the gods and the bestower of their powers, the support of the universe, He who, in the beginning, gave birth to Hiranyagarbha—may He endow us with clear intellect!"
Brahma didn’t know what for he emerged. He didn’t have the knowledge of what to create and how to create. Then he took the refuge of his own creator viz. Mahadeva, and worshiped him. Being pleased by his devotion, Rudra, bestowed Brahma, with the knowledge of creation as stated below.
“sargaadikaale bhagavaanviri~nchirupaasyaina.n sargasaamarthyamaapya | ” (Dakshinamurty Upanishad 1:20)
“At the beginning of creation, Brahmâ the Lord, having worshipped S’iva, attained power to create and was delighted at heart”.
How did he bestow that knowledge of creation? The answer is Rudra gave him Vedas as stated below.
“yo brahmaaNa.n vidadhaati puurva.n | yo vai vedaa.nshcha prahiNoti tasmai .ta.n ha devaM aatmabuddhiprakaashaM | mumuxurvai sharaNamahaM prapadye |” (Svetaswatara Upanishad 6:18)
“Seeking Liberation, I take refuge in the Lord, the revealer of Self-Knowledge, who in the beginning created Brahma and delivered the Vedas to Him”.
Shiva bestowed Brahma with Vedas and made him capable of creating the world.
“shemushhii dakshiNaa proktaa saa yasyaabhiikshaNe mukham.h | dakshiNaabhimukhaH proktaH shivo.asau brahmavaadibhiH |” (Dakshinamurty Upanishad 19)
“The word 'Dakshinâ' means Buddhi. Because Buddhi is the eye by which Siva can be directly seen, He is called Dakshinabhimtikha by the Brahma-vâdins”.
Brahmanda Purana describes Lord Shiva as ‘Kameshwara’ and Lalita as ‘Kameshwari’. In Lalita Sahasranama Stotra the following references of lord Shiva’s name as Kameshwara are found.
Verse 52: “śiva kāmeśvara aṅgasthā” – she who sits on the lap of Kameswara (shiva)
Verse 77: “kāmeśvara mukha āloka kalpita śrīgaṇeśvarā” – she who created Ganesha by the mere look of the face of her Lord , Kameshwara
Verse 82: “kāmeśvara astra nirdagdha sabhaṇḍa asura śūnyakā” – she who destroyed Bandasura and his city called sunyaka by the Kameshwara arrow.
Rig Veda’s nasadiya sukta says that the cause of the universe (hiranyagarbha) itself is ‘Kama’ as cited below.
“kāmastadaghre samavartatādhi manaso retaḥ prathamaṃ yadāsīt ||” (Rig Veda 10:129:4)
“Thereafter rose Desire (kāma) in the beginning, Desire, the primal seed (retaḥ) and germ of Spirit”.
What is that desire (kāma) which was the primal seed (retaḥ) and which became instrumental in the creation of the original egg (Hiranyagarbha) which contains all the universes? Who was that original god of desire whose desire (Kama) created the universe? It was that lord Shiva, who is beyond all attributes, and is the unborn supreme reality, who was the original Kama and because he is the ‘lord’ of the entire universe, he is ‘Ishwara’; hence it is he who is called as ‘kama ishwara’ or simply ‘kameshwara’. It was he who by resorting to his Shakti Lalita became instrumental in being the cause of the universe. Therefore Lalita being the consort of him she is called as ‘Kameshwari’.
So above verses makes it clear that lord dakshinamurti is the gurutattva(heavy/teacher/important/influential) and Lord Kameshwara is the akarshan tattwa(attraction/desire). So combining this two tattwas we get guruttwa akarshan which is gravity. Thus lord shiva is the lord of gravity.
Again, lord shiva is called the mahakala. Where in sanskrit kala has 3 meanings - time, death and black (space) so lord shiva is also the lord of time and space and death.
Here is the quote from chapter six of Shiva Gita.
“prāṇaḥ kālastathā mṛtyuramṛtaṁ bhūtamapyahama | bhavyaṁ bhaviṣyatkṛtsnaṁ ca viśvaṁ sarvātmakō’pyahama |” (Shiva Gita 6:26)
“I’m the Prana (life force), I’m the time, death, and eternity. I’m the past, present and future. I’m everything indeed!”
In the Anusasana Parva of Mahabharata there is a great eulogy by legendary sage Tandi to lord Shiva where he clearly mentions that lord Shiva is the Kala as follows.
“tvattaḥ pravartatē sarvaṁ tvayi sarvaṁ pratiṣṭhitam kālākhyaḥ puruṣākhyaśca brahmākhyaśca tvamēva hi |” (MBH 13:16:15)
“From thee flows everything. Upon thee rests everything. Thou art called Kala, thou art called Purusha, thou art called Brahma”.
Finally, let me quote Shruti also which agrees to the fact that Kala is Bhagawan Rudra alone. Here is what Taittiriya Aranyaka of Yajurveda states while praising Vamadeva (Shiva’s northward facing face) as follows.
“vāmadēvāya namō jyēṣṭhāya namaḥ śrēṣṭhāya namō rudrāya namaḥ kālāya namaḥ kalavikaraṇāya namō |” (Taittiriya Aranyaka 10.18.1)
“Salutation to Vamadeva. Salutation to Jyestha (the Eldest, existing before creation). Salutation to Srestha (the most worthy and excellent). Salutation to Rudra. Salutation to Kala. Salutation to Kalavikarana (He who causes changes in the evolution of the universe beginning with Prakriti)”.
So from above verses it is proved that lord shiva is the lord of time, death and space(eternity).
Various theories of blackholes says that universes arises and later goes into black holes. Blackholes might have multiverses inside it. So it is also same with lord shiva universes arises and ultimately goes into him during pralaya and he is the source and have multiverses inside him so he is called as Sthanu.
“sa viśvakṛd viśvavidātmayōnirjñaḥ kālakālō guṇī sarvavid yaḥ | pradhānakṣētrajñapatirguṇēśaḥ >saṁsāramōkṣasthitibandhahētuḥ |” (Ṣvētāṣvatāra Upaniṣad 6:16)
“He (i.e., Rudra) makes all, he knows all, the self-caused, the knower, the time of time (destroyer of time), who assumes qualities and knows everything, the master of nature and of man, the lord of the three qualities (guna), the cause of the bondage, the existence, and the liberation of the world”.
Etymologically ‘sthāṇu’ means – ‘pillar’, ‘immovable’, ‘fixed’, ‘pole’, ‘trunk’, ‘stationary’. It has the same origins as that of the word ‘sthūṇa’ which etymologically means, – ‘pillar’, ‘post’.
The name ‘sthāṇu’ thus means – “he who is a pillar which cannot move because of having filled everything by himself and there is no place left outside him to pervade further”. In line with this point, mahAbhArata defines his name ‘sthāṇu’ as follows. So, it is clearly because he is the infinite brahman which has filled everything hence doesn’t have any palce further to move and hence he is called a ‘pillar’ which is infinite to measure, hence everlasting.
“mahat pūrve sthito yacca prāṇotpattisthitasca yat । sthitaliṅgaśca yannityaṃ tasmāt sthāṇuriti smṛtaḥ ॥” (MBH 07:202:133)
“And since he is great and ancient and is the source of life and of its continuance, and since his linga-emblem is fixed (motionless) and is everlasting, he is for that reason called Sthanu”.
So from above verses it is proved that lord shiva is the destroyer of everything and everything is in him only so he is standing still and called as ''sthanu".
Again, "A black hole can be formed by the death of a massive star. When such a star has exhausted the internal thermonuclear fuels in its core at the end of its life, the core becomes unstable and gravitationally collapses inward upon itself, and the star's outer layers are blown away." So in other word basically a blackhole kills a star(sun).
In Puranas we can find a story of lord Shiva killing lord Surya as a result he got the curse of killing his own son from the sage Kashyapa though later he resurrected the sun god. (See this question).
Conclusion.: Lord Shiva is the Lord of Blackholes.