A team of physicists has discovered a new approach that redefines the conception of black holes by mapping out their detailed structure, as shown in a research study recently published in Journal of High Energy Physics.
The study details new theoretical structures called "supermazes" that offer a more universal picture of black holes to the field of theoretical physics. Based in string theory, supermazes are pivotal to understanding the structure of black holes on a microscopic level.
"General relativity is a powerful theory for describing the large-scale structure of black holes, but it is a very, very blunt instrument for describing black-hole microstructure," said Nicholas Warner, co-author of the study and professor of physics, astronomy and mathematics at the USC Dornsife College of Letters, Arts and Sciences. In a framework of theories extending beyond Einstein's equations, supermazes provide a detailed portrait of the microscopic structure of brane black holes.
Reinventing the black hole
Black holes are objects whose gravity is strong enough to trap light, and the traditional black hole of general relativity is surrounded by an event horizon. Seen from outside the event horizon, such a black hole is featureless - but this is fundamentally inconsistent with quantum mechanics. Within the purview of quantum gravity, which transcends general relativity, black holes must exhibit a vast amount of microstructure.
String theory can achieve this by replacing traditional black holes by conceptual objects known as "fuzzballs." Warner's work shows how one can actually construct fuzzballs from supermazes of physical objects in higher-dimensional spacetime, creating an object that behaves like a black hole and yet exhibits all its structure.
"Suppose you wanted a picture of Michelangelo's Last Judgment: General relativity, with its horizons, is like using a camera with only one pixel," Warner said. "All you see is a single smear of color. Our earlier work gave us a picture with maybe 1,000 pixels: outlines of structures and some of the shading. Supermazes are like having many, many billions of pixels enabling us to admire the masterpiece in detail."
Supermazes recreate black holes in M-theory
The new research is centered in M-theory, a theoretical framework in physics that is related to string theory. M-theory posits that strings - the fundamental building blocks of the universe - aren't one-dimensional. Instead, they exist in higher dimensions as "branes," short for membranes, which are physical objects that extend in multiple spatial dimensions. Branes have multidimensional surfaces that play a critical role in string theory and M-theory.
"In this paper, we explore intersecting systems of M2-branes (two-dimensional) and M5-branes (five-dimensional) within the realm of supergravity, which is a low-energy approximation of M-theory," Warner said. "We think of the maze as the 'substrate' upon which all the information about whatever made the black hole, or ever fell into it, can be encoded."
By investigating the maze function that governs these brane intersections, the study reveals how mazes have the capacity to reproduce black hole entropy and potentially describe black hole microstates.
A new approach to mapping out black holes
Brane intersections have been widely studied in string theory, but the new paper re-engineers these ideas to give new geometries that can describe black holes. The study develops a "maze function," a new mathematical construct that characterizes solutions for intersecting systems of M2 and M5 branes in supergravity. The maze function must obey a nonlinear differential equation similar to the famous Monge-Ampère equation, which governs the geometry and dynamics of M2 and M5 brane intersections.
"Maze functions play a pivotal role in linking the brane configurations to supergravity solutions, which in turn provide a new way to explore black-hole microstates," Warner said. "The maze function is the billion-pixel camera that can give us a deep and detailed picture of the microstructure of black holes."
Warner said this is just the first step in a larger program to develop a comprehensive string theory description of brane black hole's microstructure.
About the study: In addition to Warner, other researchers include Iosif Bena from Institut de Physique Théorique, Université Paris-Saclay, France; Anthony Houppe from Institut für Theoretische Physik, ETH Zürich, Switzerland; and Dimitrios Toulikas from Institut de Physique Théorique, Université Paris-Saclay, France.
The study was supported by European Research Council Grant 787320-QBH and Department of Energy Grant DE-SC0011687.
