The universal thermodynamic properties of Extremely Compact Objects*

Extremely compact objects (ECOs), defined as astrophysical objects lacking a horizon and with radii marginally outside their Schwarzschild radius, are the focus of this study. We demonstrate that in d+1 dimensions, an ECO whose surface is at a proper distance s << (M/m_p) ^2/(d-2)(d+1)l_p  outside the horizon radius of the corresponding black hole, exhibits thermodynamic characteristics akin to the semiclassical black hole of equivalent mass M where m_p and l_p are planck mass and planck length respectively.

Stephen Hawking found that black holes have a temperature, now called Hawking temperature in his honor, and our investigation reveals that ECOs, at leading order, show similar thermodynamic properties like the Hawking temperature, entropy, and radiation rates, comparable to their equivalent semiclassical black holes. An important aspect of our argument comprises of demonstrating the inability of the Tolman-Oppenheimer-Volkoff equation to yield consistent solutions within the vicinity immediately exterior to the ECO's surface, unless this region is filled with radiation of the Hawking temperature with appropriate blueshift. 

Insights from string theory tell us the notion of black hole microstates as fuzzballs, devoid of horizons and with radii marginally outside their Schwarzschild radius. Horizon of a semiclassical black hole led to one of the most famous puzzles in physics, the Hawking's black hole information paradox. Thus, our findings provide a seamless closure to the fuzzball paradigm which replaces conventional black holes by horizonless fuzzballs; the absence of a horizon in a fuzzball mitigates the paradox, while the thermodynamic attributes of semiclassical black holes are remarkably preserved through the ECO argument, thereby fortifying our understanding of these cosmic objects.