# Violation of unitarity by Hawking radiation does not violate energy-momentum conservation

## Abstract

An argument by Banks, Susskind and Peskin (BSP), according to which violation of unitarity would violate either locality or energy-momentum conservation, is widely believed to be a strong argument against non-unitarity of Hawking radiation. We find that the whole BSP argument rests on the crucial assumption that the Hamiltonian is not highly degenerate, and point out that this assumption is not satisfied for systems with many degrees of freedom. Using Lindblad equation, we show that high degeneracy of the Hamiltonian allows local non-unitary evolution without violating energy-momentum conservation. Moreover, since energy-momentum is the source of gravity, we argue that energy-momentum is necessarily conserved for a large class of non-unitary systems with gravity. Finally, we explicitly calculate the Lindblad operators for non-unitary Hawking radiation and show that they conserve energy-momentum.

- Authors:

- Theoretical Physics Division, Rudjer Bošković Institute, P.O.B. 180, HR-10002 Zagreb (Croatia)

- Publication Date:

- Sponsoring Org.:
- SCOAP3, CERN, Geneva (Switzerland)

- OSTI Identifier:
- 22454535

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 04; Other Information: PUBLISHER-ID: JCAP04(2015)002; OAI: oai:repo.scoap3.org:9836; Article funded by SCOAP3. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 License. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; BLACK HOLES; DEGREES OF FREEDOM; GALACTIC EVOLUTION; GRAVITATION; HAMILTONIANS; INVARIANCE PRINCIPLES; QUANTUM FIELD THEORY; UNITARITY

### Citation Formats

```
Nikolić, Hrvoje.
```*Violation of unitarity by Hawking radiation does not violate energy-momentum conservation*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/04/002.

```
Nikolić, Hrvoje.
```*Violation of unitarity by Hawking radiation does not violate energy-momentum conservation*. United States. doi:10.1088/1475-7516/2015/04/002.

```
Nikolić, Hrvoje. Thu .
"Violation of unitarity by Hawking radiation does not violate energy-momentum conservation". United States.
doi:10.1088/1475-7516/2015/04/002.
```

```
@article{osti_22454535,
```

title = {Violation of unitarity by Hawking radiation does not violate energy-momentum conservation},

author = {Nikolić, Hrvoje},

abstractNote = {An argument by Banks, Susskind and Peskin (BSP), according to which violation of unitarity would violate either locality or energy-momentum conservation, is widely believed to be a strong argument against non-unitarity of Hawking radiation. We find that the whole BSP argument rests on the crucial assumption that the Hamiltonian is not highly degenerate, and point out that this assumption is not satisfied for systems with many degrees of freedom. Using Lindblad equation, we show that high degeneracy of the Hamiltonian allows local non-unitary evolution without violating energy-momentum conservation. Moreover, since energy-momentum is the source of gravity, we argue that energy-momentum is necessarily conserved for a large class of non-unitary systems with gravity. Finally, we explicitly calculate the Lindblad operators for non-unitary Hawking radiation and show that they conserve energy-momentum.},

doi = {10.1088/1475-7516/2015/04/002},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 04,

volume = 2015,

place = {United States},

year = {Thu Apr 02 00:00:00 EDT 2015},

month = {Thu Apr 02 00:00:00 EDT 2015}

}