BUG: TypeError when subtracting datetime series from NaT series

[torfsen]

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Reproducible Example

import pandas as pd
pd.Series([pd.to_datetime('')]) - pd.Series([pd.to_datetime('2000-01-01 00:00 +00:00')])

Issue Description

When subtracting an all-NaT series from a tz-aware datetime64 series, a TypeError is raised:

Traceback (most recent call last):
  File "/home/fbrucker/apps/pyenv/versions/test-pandas/lib/python3.9/site-packages/pandas/core/arrays/datetimes.py", line 732, in _sub_datetime_arraylike
    self._assert_tzawareness_compat(other)
  File "/home/fbrucker/apps/pyenv/versions/test-pandas/lib/python3.9/site-packages/pandas/core/arrays/datetimes.py", line 711, in _assert_tzawareness_compat
    raise TypeError(
TypeError: Cannot compare tz-naive and tz-aware datetime-like objects.

The above exception was the direct cause of the following exception:

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/home/fbrucker/apps/pyenv/versions/test-pandas/lib/python3.9/site-packages/pandas/core/ops/common.py", line 70, in new_method
    return method(self, other)
  File "/home/fbrucker/apps/pyenv/versions/test-pandas/lib/python3.9/site-packages/pandas/core/arraylike.py", line 108, in __sub__
    return self._arith_method(other, operator.sub)
  File "/home/fbrucker/apps/pyenv/versions/test-pandas/lib/python3.9/site-packages/pandas/core/series.py", line 5636, in _arith_method
    return base.IndexOpsMixin._arith_method(self, other, op)
  File "/home/fbrucker/apps/pyenv/versions/test-pandas/lib/python3.9/site-packages/pandas/core/base.py", line 1295, in _arith_method
    result = ops.arithmetic_op(lvalues, rvalues, op)
  File "/home/fbrucker/apps/pyenv/versions/test-pandas/lib/python3.9/site-packages/pandas/core/ops/array_ops.py", line 216, in arithmetic_op
    res_values = op(left, right)
  File "/home/fbrucker/apps/pyenv/versions/test-pandas/lib/python3.9/site-packages/pandas/core/ops/common.py", line 70, in new_method
    return method(self, other)
  File "/home/fbrucker/apps/pyenv/versions/test-pandas/lib/python3.9/site-packages/pandas/core/arrays/datetimelike.py", line 1340, in __sub__
    result = self._sub_datetime_arraylike(other)
  File "/home/fbrucker/apps/pyenv/versions/test-pandas/lib/python3.9/site-packages/pandas/core/arrays/datetimes.py", line 735, in _sub_datetime_arraylike
    raise type(error)(new_message) from error
TypeError: Cannot subtract tz-naive and tz-aware datetime-like objects.

Expected Behavior

I would have expected the result to be NaT, without any error.

In my particular use case, I convert user-provided string timestamps to datetimes via pd.to_datetime. The string timestamps have a tz-marker (i.e. +00:00), so they get converted to tz-aware timestamps. However, some string timestamps are empty and hence get converted to NaT.

I've tried making the all-NaT series tz-aware, but that doesn't seem to work either:

>>> pd.Series([pd.to_datetime('')]).tz_convert('UTC')
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/home/fbrucker/apps/pyenv/versions/test-pandas/lib/python3.9/site-packages/pandas/core/generic.py", line 9808, in tz_convert
    ax = _tz_convert(ax, tz)
  File "/home/fbrucker/apps/pyenv/versions/test-pandas/lib/python3.9/site-packages/pandas/core/generic.py", line 9790, in _tz_convert
    raise TypeError(
TypeError: index is not a valid DatetimeIndex or PeriodIndex

#11718 is a similar issue but has long been fixed.

Installed Versions

INSTALLED VERSIONS

commit : bb1f651
python : 3.9.9.final.0
python-bits : 64
OS : Linux
OS-release : 5.4.0-99-generic
Version : #112-Ubuntu SMP Thu Feb 3 13:50:55 UTC 2022
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 1.4.0
numpy : 1.22.2
pytz : 2021.3
dateutil : 2.8.2
pip : 21.3.1
setuptools : 59.8.0
Cython : None
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : None
IPython : None
pandas_datareader: None
bs4 : None
bottleneck : None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : None
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlwt : None
zstandard : None

[simonjayhawkins]

I've tried making the all-NaT series tz-aware, but that doesn't seem to work either:

specifying the dtype explicitly would work

s2 = pd.Series([pd.to_datetime("2000-01-01 00:00 +00:00")])
s1 = pd.Series([pd.to_datetime("")], dtype=s2.dtype)
s1 - s2

0   NaT
dtype: timedelta64[ns]

but agreed, I'm not sure whether being strict and raising when subtracting an all-NaT tz-naive series from a tz-aware datetime64 series is the correct thing to do. @jbrockmendel wdyt?

[jbrockmendel]

being strict and raising when subtracting an all-NaT tz-naive series from a tz-aware datetime64 series is the correct thing to do

tznaive - tzaware should always raise