Inconsistent index between plain DataFrame and read_sql DataFrame
- [ ] closes #47608 
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- [ ] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
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- [ ] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

ok. I try to search other method. 

 Hi @phofl, when I try this.
1)
```
data = {"a": [], "b": []}
exp = pd.DataFrame(data, columns=["a", "b"])
print(exp)
print(exp.index)
```
```
Empty DataFrame
Columns: [a, b]
Index: []
RangeIndex(start=0, stop=0, step=1)
```
2)
```
data = {1: ["foo"], 2: ["bar"]}
exp = pd.DataFrame(data, columns=["a", "b"])
print(exp)
print(exp.index)
```
```
Empty DataFrame
Columns: [a, b]
Index: []
Index([], dtype='object')
```

On current main branch, index type created is not same. Is this expected? 
 Can you create an overview of all possible cases and then add it to the issue? We should aim for consistency if we make a change

E.g. reading empty csv for example should be consistent too Hi @phofl  Possible cases of empty dataframe is as follow. I based on documentation  
```
class pandas.DataFrame(data=None, index=None, columns=None, dtype=None, copy=None)

Parameters
    data : ndarray (structured or homogeneous), Iterable, dict, or DataFrame
           Dict can contain Series, arrays, constants, dataclass or list-like objects. If data is a dict, column order follows insertion- 
           order. If a dict contains Series which have an index defined, it is aligned by its index.
```
1. Iterable
```
data = []
df = pd.DataFrame(data, columns=["A", "B"])
print(df.index)

Index([], dtype='object')
```
2. Dict

a) using series
```
data = {'a': pd.Series([]), 'B': pd.Series([])}
df = pd.DataFrame(data, columns=["A", "B"])
print(df.index)

RangeIndex(start=0, stop=0, step=1)
```
b) using list
```
data = {"A": [], "B": []}
df = pd.DataFrame(data)
print(df.index)

RangeIndex(start=0, stop=0, step=1)
```
c) using array
```
data = {'A': np.array([]), 'B': np.array([])}
df = pd.DataFrame(data)
print(df.index)
```
d) based on columns
```
data = {1: ["foo"], 2: ["bar"]}
df = pd.DataFrame(data, columns=["A", "B"])
print(df.index)

Index([], dtype='object')
```

4. Read csv
```
df = pd.read_csv("empty.csv")
print(df.index)

Index([], dtype='object')
``` Based on https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.html, 
```
index  : Index or array-like
         Index to use for resulting frame. Will default to RangeIndex if no indexing information part of input data and no index 
         provided.
```
The default is RangeIndex  when no index provided Thanks for your investigation so far @weikhor! I think your findings also intersect with https://github.com/pandas-dev/pandas/issues/47959 so would be good to document your findings there as well.

I think this topic needs more discussion in the issues before moving forward with a fix, so closing. But thanks for your effort here so far.  