Black Holes Have More States than Those Defined by the Bekenstein–Hawking Entropy: A Simple Argument
It is often assumed that the maximum number of independent states a black hole may contain is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>N</mi><mrow><mi>B</m...
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2024-12-01
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| author | Carlo Rovelli |
| author_facet | Carlo Rovelli |
| author_sort | Carlo Rovelli |
| collection | DOAJ |
| description | It is often assumed that the maximum number of independent states a black hole may contain is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>N</mi><mrow><mi>B</mi><mi>H</mi></mrow></msub><mo>=</mo><msup><mi>e</mi><msub><mi>S</mi><mrow><mi>B</mi><mi>H</mi></mrow></msub></msup></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>S</mi><mrow><mi>B</mi><mi>H</mi></mrow></msub><mo>=</mo><mi>A</mi><mo>/</mo><mn>4</mn></mrow></semantics></math></inline-formula> is the Bekenstein–Hawking entropy and <i>A</i> is the horizon area in Planck units. I present a simple and straightforward argument showing that the number of states that can be distinguished by local observers inside the hole must be greater than this number. |
| format | Article |
| id | doaj-art-cf6c8c17a1ff46c98599b87d75aa599a |
| institution | Kabale University |
| issn | 2218-1997 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj-art-cf6c8c17a1ff46c98599b87d75aa599a2025-01-24T13:51:27ZengMDPI AGUniverse2218-19972024-12-01111610.3390/universe11010006Black Holes Have More States than Those Defined by the Bekenstein–Hawking Entropy: A Simple ArgumentCarlo Rovelli0CPT, Aix-Marseille Université, Université de Toulon, CNRS, Case 907, F-13288 Marseille, FranceIt is often assumed that the maximum number of independent states a black hole may contain is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>N</mi><mrow><mi>B</mi><mi>H</mi></mrow></msub><mo>=</mo><msup><mi>e</mi><msub><mi>S</mi><mrow><mi>B</mi><mi>H</mi></mrow></msub></msup></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>S</mi><mrow><mi>B</mi><mi>H</mi></mrow></msub><mo>=</mo><mi>A</mi><mo>/</mo><mn>4</mn></mrow></semantics></math></inline-formula> is the Bekenstein–Hawking entropy and <i>A</i> is the horizon area in Planck units. I present a simple and straightforward argument showing that the number of states that can be distinguished by local observers inside the hole must be greater than this number.https://www.mdpi.com/2218-1997/11/1/6black hole entropyinformation paradoxBekenstein Hawking entropy |
| spellingShingle | Carlo Rovelli Black Holes Have More States than Those Defined by the Bekenstein–Hawking Entropy: A Simple Argument Universe black hole entropy information paradox Bekenstein Hawking entropy |
| title | Black Holes Have More States than Those Defined by the Bekenstein–Hawking Entropy: A Simple Argument |
| title_full | Black Holes Have More States than Those Defined by the Bekenstein–Hawking Entropy: A Simple Argument |
| title_fullStr | Black Holes Have More States than Those Defined by the Bekenstein–Hawking Entropy: A Simple Argument |
| title_full_unstemmed | Black Holes Have More States than Those Defined by the Bekenstein–Hawking Entropy: A Simple Argument |
| title_short | Black Holes Have More States than Those Defined by the Bekenstein–Hawking Entropy: A Simple Argument |
| title_sort | black holes have more states than those defined by the bekenstein hawking entropy a simple argument |
| topic | black hole entropy information paradox Bekenstein Hawking entropy |
| url | https://www.mdpi.com/2218-1997/11/1/6 |
| work_keys_str_mv | AT carlorovelli blackholeshavemorestatesthanthosedefinedbythebekensteinhawkingentropyasimpleargument |