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Black Hole Mergers in Holographic Space-time Models of Inflation

Anish Suresh, Tom Banks

TL;DR

This work tests a key prediction of holographic space-time (HST) models of inflation: whether primordial black holes (PBHs) formed in the early matter-dominated era can merge in a way that would leave observable imprints. Using a 3D toroidal lattice with expansion and a momentum-conserving merger rule, the authors find no BH mergers under a range of plausible parameter choices. Remarkably, the dynamics drive the formation of bound structures composed of BH remnants, with macroscopic scales that could approach horizon-size features at the onset of the radiation era; the current model estimates these structures to be around $10^{28}$ in Planck units or about $10^{-4}$ cm, though their fate depends on decay products and cooling processes. Overall, the results support the viability of the HST inflation framework and motivate further investigation into the astrophysical implications of BH remnants and their potential role in early structure formation.

Abstract

Holographic space-time, a theory of quantum gravity that generalizes string theory and quantum field theory, predicts black holes in the early matter-dominated era of its models of inflation. Before these black holes can decay, there is a chance that enough of these particles merge to produce radiation visible today in the Cosmic Microwave background. To discover if this is the case, we perform a rudimentary computer simulation. We show that no problematic black holes are formed by mergers in the Holographic Space-time models of inflation. However, we conclude that tiny bound structures containing black holes remnants form in this theory unconditionally. Since black hole decay products are mostly massive standard model particles, and perhaps their superpartners, the fate of these structures is a complicated dynamical problem that requires further study. It suggests the possibility of primordial structures on the order of the horizon size at the beginning of the radiation dominated era. This is about $10^9\ L_P$ in the current model.

Black Hole Mergers in Holographic Space-time Models of Inflation

TL;DR

This work tests a key prediction of holographic space-time (HST) models of inflation: whether primordial black holes (PBHs) formed in the early matter-dominated era can merge in a way that would leave observable imprints. Using a 3D toroidal lattice with expansion and a momentum-conserving merger rule, the authors find no BH mergers under a range of plausible parameter choices. Remarkably, the dynamics drive the formation of bound structures composed of BH remnants, with macroscopic scales that could approach horizon-size features at the onset of the radiation era; the current model estimates these structures to be around in Planck units or about cm, though their fate depends on decay products and cooling processes. Overall, the results support the viability of the HST inflation framework and motivate further investigation into the astrophysical implications of BH remnants and their potential role in early structure formation.

Abstract

Holographic space-time, a theory of quantum gravity that generalizes string theory and quantum field theory, predicts black holes in the early matter-dominated era of its models of inflation. Before these black holes can decay, there is a chance that enough of these particles merge to produce radiation visible today in the Cosmic Microwave background. To discover if this is the case, we perform a rudimentary computer simulation. We show that no problematic black holes are formed by mergers in the Holographic Space-time models of inflation. However, we conclude that tiny bound structures containing black holes remnants form in this theory unconditionally. Since black hole decay products are mostly massive standard model particles, and perhaps their superpartners, the fate of these structures is a complicated dynamical problem that requires further study. It suggests the possibility of primordial structures on the order of the horizon size at the beginning of the radiation dominated era. This is about in the current model.
Paper Structure (18 sections, 17 equations, 3 figures, 1 table)

This paper contains 18 sections, 17 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Code Structure and Parameters
  3. Parameters of the Simulation
  4. Velocity
  5. Mass
  6. Initial Time
  7. Spatial Distribution and Density
  8. Updating Position and Velocity
  9. Periodic Boundary Conditions
  10. Merger Process
  11. Expansion of the Universe
  12. Time Step
  13. Results Inside Each Cell
  14. Macroscopic Behavior
  15. Expansion Time
  16. ...and 3 more sections

Figures (3)

  • Figure 1: An example to illustrate how forces travel in $\mathbb{T}^{1}$. There is one boundary black hole on the left and one interior black hole exactly in the middle. Due to the topology, the former can be thought of as being on the right, which we have modelled with a mirror black hole on the right. Forces have periodic boundary conditions as well, so this topology keeps the interior black hole in place, which in turn keeps the stationary black hole in place. This scenario is drastically different than one in $\mathbb{R}^{1}$, in which the black holes would have gravitated towards each other. Identically, we can think of the force on the right to be from the same black hole, but in the opposite boundary side.
  • Figure 2: The 3D toroidal lattice structure at $t = t_{0}$ with $N = 27$. Here, we have $13$ boundary black holes (in black), which we model on the corresponding diametrically opposite side as $13$ mirror black holes (in gray). We also have one interior black hole (in blue).
  • Figure 3: Position $x$ (blue) and Mass $M$ (red) with respect to time. Clearly, $x$ reaches 0 around $t = 3 \times 10^{13}$. Notice that mass increases with time. In fact, it is linear.