# Emergent Gravity Simulations for Schwarzschild–de Sitter Scenarios

## Abstract

**:**

## 1. Introduction

## 2. Effective Graviton Interaction

## 3. Simulation Setup

- Does spacetime curvature, i.e., a gravitational field in terms of a radial graviton density gradient, emerge upon introducing a mass (a graviton condensate) into a flat graviton background?
- Does the introduction of a test mass into a spherically symmetric gravitational field (a graviton density gradient) induce a geodesic trajectory (free fall)?

## 4. Results

#### 4.1. Spacetime Curvature

#### 4.2. Geodesic Trajectory

## 5. Discussion

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Recursive linear connection between radial graviton density $\rho $ and radial graviton velocity c for an effective Schwarzschild–de Sitter spacetime.

**Figure 2.**Time-averaged number of constituents (gravitons) per cell before (black dots) and after (blue crosses) 1000 iterations for Scenario (1).

**Figure 3.**Time-averaged number of constituents (gravitons) per cell before (black dots) and after (blue crosses) 1000 iterations for Scenario (2), for four values of the acceleration term in simulation units $\mathsf{\Delta}r/{\left(\mathsf{\Delta}t\right)}^{2}$.

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**MDPI and ACS Style**

Keppens, A.
Emergent Gravity Simulations for Schwarzschild–de Sitter Scenarios. *Foundations* **2023**, *3*, 231-240.
https://doi.org/10.3390/foundations3020019

**AMA Style**

Keppens A.
Emergent Gravity Simulations for Schwarzschild–de Sitter Scenarios. *Foundations*. 2023; 3(2):231-240.
https://doi.org/10.3390/foundations3020019

**Chicago/Turabian Style**

Keppens, Arno.
2023. "Emergent Gravity Simulations for Schwarzschild–de Sitter Scenarios" *Foundations* 3, no. 2: 231-240.
https://doi.org/10.3390/foundations3020019