Abstract
The no-hair theorem characterizes the fundamental nature of black holes in general relativity. This theorem can be tested observationally by measuring the mass and spin of a black hole as well as its quadrupole moment, which may deviate from the expected Kerr value. Sgr A*, the supermassive black hole at the center of the Milky Way, is a prime candidate for such tests thanks to its large angular size, high brightness, and rich population of nearby stars. In this paper, I discuss a new theoretical framework for a test of the no-hair theorem that is ideal for imaging observations of Sgr A* with very long baseline interferometry (VLBI). The approach is formulated in terms of a Kerr-like spacetime that depends on a free parameter and is regular everywhere outside of the event horizon. Together with the results from astrometric and timing observations, VLBI imaging of Sgr A* may lead to a secure test of the no-hair theorem.
Highlights
Tim JohannsenPhysics Department, University of Arizona, 1118 E. 4th Street, Tucson, AZ 85721, USA
According to the no-hair theorem, black holes are uniquely characterized by their masses and spins and are described by the Kerr metric [1,2,3,4,5,6]
If no deviation is detected, the compact object is a Kerr black hole. Since such deviations can have a significant impact on the observed signals, the no-hair theorem may be tested in a twofold manner: if a deviation is measured to be nonzero and if general relativity is assumed, the object cannot be a black hole [18, 35]
Summary
Physics Department, University of Arizona, 1118 E. 4th Street, Tucson, AZ 85721, USA. The no-hair theorem characterizes the fundamental nature of black holes in general relativity. This theorem can be tested observationally by measuring the mass and spin of a black hole as well as its quadrupole moment, which may deviate from the expected Kerr value. Sgr A∗, the supermassive black hole at the center of the Milky Way, is a prime candidate for such tests thanks to its large angular size, high brightness, and rich population of nearby stars. I discuss a new theoretical framework for a test of the no-hair theorem that is ideal for imaging observations of Sgr A∗ with very long baseline interferometry (VLBI). Together with the results from astrometric and timing observations, VLBI imaging of Sgr A∗ may lead to a secure test of the no-hair theorem
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