The Holographic Nature of Null Infinity
We argue that, in a theory of quantum gravity in a four dimensional asymptotically flat spacetime, all information about massless excitations can be obtained from an infinitesimal neighbourhood of the past boundary of future null infinity and does not require observations over all of future null inf...
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| Published in | SciPost physics Vol. 10; no. 2; p. 041 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
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18.02.2021
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| Online Access | Get full text |
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| Abstract | We argue that, in a theory of quantum gravity in a four dimensional asymptotically flat spacetime, all information about massless excitations can be obtained from an infinitesimal neighbourhood of the past boundary of future null infinity and does not require observations over all of future null infinity. Moreover, all information about the state that can be obtained through observations near a cut of future null infinity can also be obtained from observations near any earlier cut although the converse is not true. We provide independent arguments for these two assertions.
Similar statements hold for past null infinity. These statements have immediate implications for the information paradox since they suggest that the fine-grained von Neumann entropy of the state defined on a segment (-infty,u) of future null infinity is independent of u. This is very different from the oft-discussed Page curve that this entropy is sometimes expected to obey.
We contrast our results with recent discussions of the Page curve in the context of black hole evaporation, and also discuss the relation of our results to other proposals for holography in flat space. |
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| AbstractList | We argue that, in a theory of quantum gravity in a four dimensional asymptotically flat spacetime, all information about massless excitations can be obtained from an infinitesimal neighbourhood of the past boundary of future null infinity and does not require observations over all of future null infinity. Moreover, all information about the state that can be obtained through observations near a cut of future null infinity can also be obtained from observations near any earlier cut although the converse is not true. We provide independent arguments for these two assertions. Similar statements hold for past null infinity. These statements have immediate implications for the information paradox since they suggest that the fine-grained von Neumann entropy of the state defined on a segment $(-\infty,u)$ of future null infinity is independent of u. This is very different from the oft-discussed Page curve that this entropy is sometimes expected to obey. We contrast our results with recent discussions of the Page curve in the context of black hole evaporation, and also discuss the relation of our results to other proposals for holography in flat space. We argue that, in a theory of quantum gravity in a four dimensional asymptotically flat spacetime, all information about massless excitations can be obtained from an infinitesimal neighbourhood of the past boundary of future null infinity and does not require observations over all of future null infinity. Moreover, all information about the state that can be obtained through observations near a cut of future null infinity can also be obtained from observations near any earlier cut although the converse is not true. We provide independent arguments for these two assertions. Similar statements hold for past null infinity. These statements have immediate implications for the information paradox since they suggest that the fine-grained von Neumann entropy of the state defined on a segment (-infty,u) of future null infinity is independent of u. This is very different from the oft-discussed Page curve that this entropy is sometimes expected to obey. We contrast our results with recent discussions of the Page curve in the context of black hole evaporation, and also discuss the relation of our results to other proposals for holography in flat space. |
| ArticleNumber | 041 |
| Author | Prabhu, Siddharth Raju, Suvrat Shrivastava, Pushkal Laddha, Alok |
| Author_xml | – sequence: 1 givenname: Alok surname: Laddha fullname: Laddha, Alok organization: Chennai Mathematical Institute – sequence: 2 givenname: Siddharth surname: Prabhu fullname: Prabhu, Siddharth organization: Tata Institute of Fundamental Research – sequence: 3 givenname: Suvrat surname: Raju fullname: Raju, Suvrat organization: Tata Institute of Fundamental Research – sequence: 4 givenname: Pushkal surname: Shrivastava fullname: Shrivastava, Pushkal organization: Tata Institute of Fundamental Research |
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| Title | The Holographic Nature of Null Infinity |
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