# A solution to black hole information paradox

**Olayode Olalekan Babatunde**

**Email:**sylwester.kornowski@gmail.com

**Received: **14-Jun-2023, Manuscript No. puljmap-23-6521;
**Editor assigned: **16-Jun-2023, Pre QC No. puljmap-23-6521 (PQ);
**Accepted Date:** Jun 29, 2023;
**Reviewed: **18-Jun-2023 QC No. puljmap-23-6521 (Q);
**Revised: **21-Jun-2023, Manuscript No. puljmap-23-6521 (R);
**Published:**
15-Jul-2023

**Citation:** Babatunde, O. O. A Solution to Black Hole information paradox. J
Mod Appl Phys. 2023, 6(3):1-3.

This open-access article is distributed under the terms of the Creative Commons Attribution Non-Commercial License (CC BY-NC) (http://creativecommons.org/licenses/by-nc/4.0/), which permits reuse, distribution and reproduction of the article, provided that the original work is properly cited and the reuse is restricted to noncommercial purposes. For commercial reuse, contact reprints@pulsus.com

## Abstract

This is a framework to unify black hole, dark matter and dark energy as faster-than-light moving perfect fluid. Two postulates to unravel the underlying physics behind the event horizon of black hole; by the virtue of these postulates we will be able to comprehend the nature and the evaporation of black hole. I establish a relationship between second order in ricci scalar curvature and dark energy current, and show that the current is conserved.

### Key Words

Quantum; Electromagnetism; Black hole; Cosmological; Paradox

### Introduction

Since the work of Stephen Hawking black hole information paradox has been one of the most sought-after problem in theoretical physics. The hope is that a solution will reconcile the conflict between general relativity and quantum mechanics. This paper attempts at unification of black hole, dark matter and dark energy as faster-than-light moving perfect fluid. The approach to be followed in this paper is a deterministic hidden-variable description of quantum gravity and I believe that determinism gives rise to non-locality. I will try to reconcile the conflict between general relativity and quantum mechanics as much as i can. The whole ideas in this paper will heavily depend on the following two postulates that I put forward:

• It is the nature of the Ground State of a Quantum field of a black hole to be Steady.

• Speed of Light Is Quantized.

**Black hole and EPR paradox**

Suppose a spin zero particle at the event horizon of black hole as shown in **Figure1** decays into electron-positron pairs as shown in **Figure 2.** What will be the fate of the ingoing and the outgoing particles?

Particle with spin zero decays into leptons

Binomial approximation of scalar stress energy curvature T^{n}=1+ nx where , v is the velocity and c is speed of light at x = −1,T^{n}=1-n when v = 1c T^{1}= 0 ;at v = 2c, Now if is Euler characteristic at n = 2 as in (1) which describe second order in scalar stress energy curvature for sphere T^{2}=-1 and for torus T^{2}=3

The laws of physics are invariant: From Galilean transformation of Newtonian mechanics to Einsteinian relativity motion has been relative and the laws of physics are invariant but if we consider classical theory of electromagnetism relative motion is quiet not necessary and the laws of physics hold true. If we place either of the electron-positron pairs at a point in the interior of black hole and the other at a point in the photon sphere, I claim that the laws of physics are the same. The classical theory of electromagnetism does not change.

represents vacuum expectation value of cosmological constant of black hole. Special orthogonal group (2) formulation implies that det and 1-dimensional torus is isomorphic to S^{1}

The vacuum expectation value of black hole cosmological constant can be calculated as follows, where n is number of ground state.

AMPS firewall model claimed that the entanglement between ingoing and outgoing Hawking radiation is broken once the ingoing particle crosses the event horizon which creates firewall on the event horizon of a black hole ref [1-4]. EPR=ER model provided a solution by claiming the entangled particles are connected by wormhole [2-7]. The article we will look at it from different perspective, according to the first postulate “it is the nature of the ground state of a quantum field of a black hole to be steady”. by implication as the ingoing particle crosses the event horizon it distorts the steadiness of the ground state of the black hole which triggers the emission of energy which flows from the interior of black hole to the photon sphere back and forth in such a way that the current of the energy is conserved. Equation (1) showed how the speed is related to the dimension of second order in stressenergy scalar curvature tensor. The energy arises not from the disentanglement of electron-positron pairs but from the distortion of ground state of black hole this energy is what I describe as dark energy.

Dark energy current of the outgoing and incoming energy is conserved as shown in (11); in (12) and (13) creation and annihilation operator act on the energy-momentum state of black hole to create dark energy as the result of particle invading black hole.

if we substitute Einstein’s equation in (17) into second order in ricci curvature tensor we will be able to calculate the second order in ricci scalar curvature as shown in (18) and (19). The values for second order in ricci scalar in (19) and second order in stress-energy scalar curvature in (1) are similar and it is obvious that they are interchangeable.

Vacuum expectation value of cosmological constant of black hole is described as SO(2) orthogonal matrices acting on a single ground state for spin zero particle and two states for electro-positron pairs.

### Conclusion

• I unified black hole, dark matter and dark energy as faster than-light moving perfect fluid.

• Two postulates to unravel the underlying physics behind the event horizon of black hole; by the virtue of these postulates we will be able to comprehend the nature and the evaporation of black hole.

• I established a relationship between second order in ricci scalar curvature and dark energy current and I showed that the current is conserved.

• The paradox is solved within the scope of this paper.

### Acknowledgement

The mighty hands that wrote beautiful equations that only a feeble mind could understand hallowed be thy name. I want to thank my wonderful parents for their support throughout my research work. Financially, morally…In fact for all their assistance and also want to thank my reliable younger brother Taiwo for his contribution towards the success of this work and to my Wuraola, sister Jumoke and Kehinde I say thank you so much!!!

I will like to appreciate the following institutes: Perimeter Institute for Theoretical Physics: for making PSI masters’ video lectures available online. Massachusetts institute of Technology, National Program On Technology Enhanced Learning (NPTEL) Indian, Abdus Salam International Centre for Theoretical Physics (ICPT), Stanford University, Harvard University, Yale University just to mention a few: for tons of lectures in physics and mathematics available on their website and YouTube. all physics popularizers such as Dr. Brian Greene, Dr. Don Lincoln, Socratica, Dr. Michio Kaku, Dr. Sabina Hossenfelder just to mention a few. all my friends, and everyone who has put one or more physics and mathematics video on YouTube.

I also want to thank DR physics A (Bob Eagle), Dr. Sabieh Anwar, Dr. N.J. Wildberger, Dr. Frederic Schuller (FAU) for their concise lectures on YouTube. Philip Gibbs for creation of vixra and also Damilola who has been praying for me.

I say thank you!!!

### References

- Susskind L, Thorlacius L, Uglum J. The stretched horizon and black hole complementarity. Phys Rev D. 1993; 48(8):3743.
- Maldacena J, Susskind L. Cool horizons for entangled black holes. Fort der Phy. 2013; 61(9):781-811.
- Mathur SD. The fuzzball proposal for black holes: An elementary review. Fort der Phys: Progress of Physics. 2005; 53(7â?8):793-827.
- Almheiri A, Marolf D, Polchinski J, et al. Black holes: complementarity or firewalls?. J High Ener Phys. 2013; 2013(2):1-20.
- Farnes JS. A unifying theory of dark energy and dark matter: Negative masses and matter creation within a modified ΛCDM framework. Astro & Astrophys. 2018; 620:A92.
- Croker KS, Nishimura KA, Farrah D. The GEODE mass function and its astrophysical implications. arXiv
- Abedi J, Dykaar H, Afshordi N. Echoes from the Abyss: Tentative evidence for Planck-scale structure at black hole horizons. Phys Rev D. 2017; 96(8):082004.
[Googlescholar] [Crossref]